So far everything has been derived from the Major Scale, but now I have some new scales to introduce. These are foreign and exotic scales with fascinating new sounds!

After RM1 as a proof of concept, RM2 introduced the Major modes and RM3 explained how they work. Now RM4 will introduce new scales and–guess what?–RM5 will explain how they work. This episode also includes a bit more information on chords.

TO THE SCALES!

(They have been right justified for easy comparison)

Symmetrical Scales:

These scales are not generally pleasing, but can be very cool to play with. They are called symmetrical because the scale formulas allow multiple degrees to be identified as the root.

Chromatic: x x x x x x x x x x x x

Whole Tone: x – x – x – x – x – x –

Diminished: x – x x – x x – x x – x

Six Tone Symmetrical: x x – – x x – – x x – –

Modified Symmetrical Scales:

Altered: x x – x x – x – x – x –

Leading Whole Tone: x – x – x – x – x x x –

Common Scales:

These are some popular western scales that make up most music nowadays.

Major: x – x – x x – x – x – x

Major Pentatonic: x – x – x – – x – x – –

Blues: x – – x x x x x – – x –

Minor Pentatonic: x – – x – x – x – – x –

Natural Minor (Aeolian): x – x x – x – x x – x –

Melodic Minor: x – x x – x – x – x – x

Harmonic Minor: x – x x – x – x x – – x

Modified Common Scales:

Lydian Flat-Seven: x – x – x – x x – x x –

Lydian Minor: x – x – x – x x x – x –

Lydian Diminished: x – x x – – x x x – x –

Overtone (Lydian Dominant): x – x – x – x x – x x –

Major Locrian: x – x – x x x – x – x –

Super Locrian: x x – x x – x – x – x –

Double Harmonic: x x – – x x – x x – – x

Nine Tone: x – x x x – x x x x – x

Auxiliary Diminished: x – x x – x x – x x – x

Auxiliary Augmented: x – x – x – x – x – x –

Auxiliary Diminished Blues: x x – x x – x x – x x –

Ethnic Scales:

These scales are a bit more rare. They tend to be tonally powerful and emphasize some interesting notes. Play in these scales and, like magic, you sound like you’re playing music from their countries of origin (more or less–mimicking the ethnic rhythm helps).

Roumanian: x – x x – – x x – x x –

Spanish Gypsy: x x – – x x – x x – x –

Eight Tone Spanish: x x – – x – x – x – x x

Neopolitan Major: x x – x – x – x – x – x

Prometheus: x – x – x – x – – x x –

Prometheus Neopolitan: x x – – x – x – – x x – –

Pelog: x x – x – – x – – – x x

Oriental: x x – x x x x – x – x –

Hungarian Major: x – – x x – x x – x x –

Iwato: x – – – x x – – – x – x

Hirajoshi: x – x x – – – x x – – –

Hindu: x – x – x x – x x – x –

Arabian: x – x – x x x – x – x –

Gypsy: x x – – x x – x x – – x

Mohammedan: x – x x – x – x x – – x

Javanese: x x – x – x – x – x – x

Persian: x x – – x x x – x – – x

Byzantine: x x – – x x – x x – – x

Hawaiian: x – x x – – – x – x – x

Mongolian: x – x – x – – x – x – –

Egyptian: x – x – – x – x – – x –

Chinese: x – – – x – x x – – – x

Scale Names and Relativity

Many scales have names that describe them relative to other scales. For example, compare the Locrian and the Major Locrian.

Locrian: x x–x– x x – x – x –

Major Locrian: x –x–x x x – x – x –

The Locrian is transformed into a Major Locrian by sharpening the 2nd and 3rd degrees (raising them 1 half-step). That change results in a scale that seems to combine the Locrian and the Unison. It combines the Locrian sound with a very “Major” sound, hence it is called the Major Locrian.

A similar modification of the Locrian mode generates the Super Locrian.

Locrian: x x – x –x x – x – x –

Super Locrian: x x – x x– x – x – x –

Every note in the Locrian mode is 1 half-step off of the Major scale (Unison mode) except for the 1st and 4th degrees which remain. By flattening the 4th, the scale is then considered Super Locrian. As you can see, the names themselves are unimportant, but help to convey the design of the scale. The Super Locrian can also be seen as equal to the Melodic Minor scale from the 7th degree.

Melodic Minor: x – x x – x – x – x – x

Super Locrian: xx – x x – x – x – x –

Robot Implementation

Just as we replaced the Major Pentatonic in RM1 with the full Major scale in RM2, we can replace the Major scale with any of these others and apply the same logic.

Where modes of the Major scale explored different sensations within that scale, these scales can explore brand new areas that don’t exist within the limitations of the Major formula. Furthermore, each of these scales has its own set of modes that emphasizes its different facets.

It’s not hard to find other scales out in the wild, but you’ll probably see that most of them are not much different from some that are already on this list. In the next installment we can go into generating our own scales so having a long list will be unnecessary. However, it’s worth playing with these scales so you have a better feel for what’s coming up. You’ll also want to be comfortable with the terminology of scales.

Scale and Chord Terminology

(Chords are described according to the scales they encompass, so this section applies to both subjects)

You’ve probably picked up on some of the terminology being thrown around. If you understand these terms, you can decipher scales and chords based on their names very easily. You can also begin describing scales and chords more accurately, including those you invent yourself.

Here are some common terms:

Triad: A chord made up of the 1st, 3rd, and 5th degrees. Generally this refers to the Major Triad (a triad in the Major Scale).

Flat: If a degree is flattened, it is lowered by 1 half-step. An example of this is the Lydian Flat-Seven Scale, which is the same as the Lydian mode, but with a flattened 7th degree.

Diminished: This refers to a degree being lowered (flattened) by 1 half-step. Generally this is in regards to the 5th degree. In other cases, the degree being diminished will be stated (e.g. Diminished 7th). In a diminished triad, the 3rd and 5th degrees are both flattened.

Major Triad: x – – –x – –x – – – –

Diminished Triad: x – – x–– x– – – – –

Augmented: An augmented interval is the opposite of a diminished one; it has been raised (sharpened) by 1 half-step. An augmented triad is the same as a Major triad but with a sharpened 5th.

Major Triad: x – – – x – – x– – – –

Augmented Triad: x – – – x – – –x – – –

Major: Major tends to mean “like the Major scale.” As mentioned above, the Major Locrian is basically a combination of the Major and Locrian scales.

Minor: Minor is usually synonymous with “flattened.” This is true in the case of the minor 2nd interval (m2, as in Cm2) where the interval is actually composed of a flattened 2nd degree (AKA a semitone). Other times it may mean “like the Minor Scale” as in the Lydian Minor Scale which is a combination of the Lydian and Minor scales. Generally the “Minor” sound is associated with a minor 3rd interval (as contained in the Minor scale). The Minor scale is sometimes called the Natural Minor to differentiate it from the Melodic Minor and Harmonic Minor, which are also characterized by a flattened 3rd degree.

Dominant: The dominant is the 5th degree. A scale or chord with the word dominant in its name may contain the 5th degree and/or be based upon the Myxolydian mode (the 5th mode) as in the case of the Lydian Dominant.

Seventh, 7, or vii: The 7th degree is an exception to some rules because when a scale or chord has a 7, that usually means it has a flat 7 (AKA minor 7). However, if a scale or chord is meant to contain the 7th degree as in the Major Scale (Unison), it will be called a Major 7. These two triads demonstrate the difference between the C7 (Cm7, Cmin7) and the C Major 7 (CM7, Cmaj7) chords:

C7: C – – – E – – G – – Bâ™­–

C Major 7: C – – – E – – G – – –B_

The minor 7 is characteristic of the Myxolydian mode. Therefore, another name for the minor 7th interval is the Dominant 7th. Since the plain old 7th usually refers to a flat 7, saying Diminished 7th is really saying “Diminished flat 7th” which equals a double-flat 7 or the 6th interval. Yes, it’s all very confusing and stupid.

Leading: A leading tone is 1 half-step lower than the note it “leads” to (the Major 7th interval). The Leading Whole Tone Scale adds a leading note between the augmented 5th and 6th degrees. Apparently the major and minor 3rds also have “latent tendencies.”

Pentatonic, Hexatonic, etc: Names like these are often using latin to describe the number of notes in the scale. Penta means 5, so a Pentatonic scale contains 5 notes. Hex means 6 so the Hexatonic contains 6 notes. This is not true in the case of the Diatonic which actually means “Progressing tones” (another name for the Major Scale).

No experiment this time around, but look forward to one in Robot Music 5, when we’ll finally start breaking some rules. We gotta teach our Robot to improvise!

-Christopher J. Rock

Notes:

http://www.musisindo.com/e107/guitarchord.htm: This is a great website for examining chords and scales on piano keys. Just enter in the chord or scale you want to see and it highlights the right keys. You can even enter in formulas for your own custom scales.

Naming Scale Degrees

As discussed in previous chapters, the names of notes are not relevant to our Robots. For that reason, I haven’t bothered to name the “accidentals” properly.

Accidentals are all the sharps and flats not included in the C Major scale. When these came up I started out using only the sharp symbol (â™¯) and then switched to flat (b) for scale degrees. I’ll quote wikipedia for the correct way to name scale degrees:

In naming the notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A diatonic scale is written A – B – Câ™¯ – D – E – Fâ™¯ – Gâ™¯ rather than A – B – Dâ™­ – D – Fâ™­ – Eâ™¯â™¯ – Gâ™¯. However, it is impossible to do this with scales containing more than seven notes.

That’s all well n’ good for some old European guy, but if you ask me it’s just making things look more complicated than they need to be. That’s why I prefer to stick to degree numbers with flats when necessary.

At first glance it is a very interesting paper. I must give it a good read! Thanks for the link.

How did you end up coming across it yourself? Are you a student of music?

Unfortunately, I’ve had so many projects going that I haven’t had the time to get to RMV, but in it, I would like to explore some of these underlying patterns. This kind of homework may come in handy (though I’m limiting this series to layman’s terms). I’d like to link to more outside sources so I do have a bit of a list going. Let me know if you have anything else up your sleeve.

fab

Sometimes I wish, I was a music student. I’m a physics student and casual guitar player. Having nothing better to do in the the summer vacation, I wanted to get more into music theory. arxiv.org is the place where academical work from the field of theoretical physics and mathematics is published and they often have an interesting paper about just anything. I came across the paper the same day I found your blog, so I decided to post the link. By the way: thank you for this lot of information in you blog!
I try to implement things I learn about music theory in a computer program. It’s a kind of note-editor, I’m writing and can be found here:http://narf.bplaced.net/synthgunt/
Up to now it’s not very usable, but I will make a better release shortly.
If you have any ideas that can go in the program, let me hear!